Judgment and Decision Making, vol. 5, no. 2, April 2010, pp.
83-101

Decisions by coin toss: Inappropriate but fair

Gideon Keren*
Tilburg University

  Karl H. Teigen
University of Oslo

In many situations of indeterminacy, where people agree that
no decisive arguments favor one alternative to another, they are
still strongly opposed to resolving the dilemma by a coin toss. The
robustness of this judgment-decision discrepancy is demonstrated in
several experiments, where factors like the importance of consequences,
similarity of alternatives, conflicts of opinion, outcome certainty,
type of randomizer, and fairness considerations are systematically
explored. Coin toss is particularly inappropriate in cases of life and
death, even when participants agree that the protagonists should have
the same chance of being saved. Using a randomizer may seem to conflict
with traditional ideas about argument-based rationality and personal
responsibility of the decision maker. Moreover, a concrete randomizer
like a coin appears more repulsive than the abstract principle of using
a random device. Concrete randomizers may, however, be admissible to
counteract potential partiality. Implications of the aversion to use
randomizers, even under circumstances in which there are compelling
reasons to do so, are briefly discussed.

Keywords: coin toss, randomizers, equipoise, decision aversion.

1  Introduction

It has been said that life is a lottery and not a chess game. Even
major events in life (like a person’s sex, health, marriage, children,
and career) are heavily influenced, if not wholly determined, by
random factors (Bandura, 1982, 1998). Yet, rational decision makers
prefer the chess game metaphor, where moves are restricted by rules
and are selected according to how well they serve initially specified
goals. Good decisions should be justifiable, that is, they should be
determined by explicit, well defined, rational and ethical
considerations, where strong and consistent reasons are given more
weight than weak and capricious ones. Thus one would not place much
credence on decisions that are simply a result of a random mechanism
like a lottery or a coin toss. A doctor who prescribes medicine by
simply opening his drug manual at random would quickly lose his
patients (and eventually his license).

Even a rational decision maker may occasionally meet choices that
cannot be resolved by reasons and arguments alone. Typical situations
are choices between two equally valuable options (should I go right or
left), or settling a dispute between two actors who both want an
advantage (who should play the white pawns). In some such situations
randomizers are accepted, and even institutionalized as tie breakers.
For instance, an old standing practice in soccer games is to toss a
coin before the start of the game in order to determine which team
will play the first half on which side and who is going to kick the
ball first. There are several reasons justifying the use of a coin in
this case: It gives both sides an equal chance and thus it is fair, it
is efficient and fast and, most important, it probably has almost no
effect on the final outcome of the game — its importance is
negligible. In contrast when the outcome is important, a coin toss
becomes less acceptable. Thus, in the 1968 European football
championship, the semi-final between Italy and the Soviet Union was
decided (after extra time) by a coin flip (Italy won and became the
European champion). The fact that such an important game was randomly
determined was so aversive that it was decided from then on to replace
the coin toss by penalty kicks.1

People’s reluctance to use a randomizer as a decision device, has been
demonstrated in field studies. Oberholzer-Gee, Bohnet and Frey (1997)
studied the social acceptability of different decision procedures,
including a lottery, to determine the sitting of nuclear waste
facilities in Switzerland. Using a large representative sample, they
asked participants to rate alternative decision procedures to
determine the place for locating future nuclear waste
repositories. Two important results emerged from their study. First,
using a lottery was located low in the list — only 26% respondents
rated this procedure as acceptable. Second, the more acceptable
methods, such as negotiations, the current method used which
ultimately requires the federal parliament approval, and handing the
decision to foreign experts, all are assumed implicitly to eventually
be reason-based.

Randomness is in particular repudiated in the legal system, which,
like rational decision making, is believed to rest entirely on reason
and reason alone. The use of an explicit randomizer, such as the coin,
is utterly forbidden. Thus, the Michigan Supreme court publicly
reprimanded a Wayne county judge for flipping a coin to decide where
two girls in a custody dispute would spend Christmas (Aschenfelter,
2003). In its decision, the court claimed that “The public’s trust
and confidence in the judiciary was damaged.” In another case, a
judge in a N.Y. City court flipped a coin to determine whether to
sentence an individual to 20 or 30 days in jail. Although the coin
flip produced an outcome in an inexpensive and prompt fashion, the
judge was censured. His critics did not complain that he had reached
the wrong decision. Rather, they complained about
process. Specifically, the critics claimed that “the coin flip
offended this society’s commitment to rationality.” Evidently,
whether or not a judge’s mental processes actually amount to anything
more than a mental coin flip, the community wishes judicial rulings to
appear to be the product of contemplative, deliberative, cognitive
processes.

There could be several reasons why people dislike the use of a coin.
First, the use of a randomizer implies relinquish of control, a
property that people rarely want to give up (Skinner, 1996). Second,
there are contexts in which the use of randomizers, coin being a par
excellence example, is associated with negative connotations such as
gambling. Third, and perhaps more important, it is expected that people
could justify their choice by adequate arguments and reasons (Shafir,
Simonson & Tversky, 1993). Fourth, they should be accountable for
their decisions (Tetlock, 1992), in particular when the consequences of
the decision are of great importance. Coins, and other randomizers,
cannot deliver appropriate reasons and cannot be regarded as
responsible agents, thus they may be objectionable both on rational and
moral grounds.

However, there are cases where the use of a randomizer is rationally
and ethically defensible, and could even be recommended. These are
situations where the decision maker is unable to attach more
importance to the arguments favoring one alternative than to the
arguments favoring the other, in short in situations of
indifference. Although rational choice theory (e.g., classical utility
theory) is rather silent about situations of indifference and never
prescribes explicitly a decision by lot, it is compatible with the
idea that a decision-maker who is unable to make up her mind should
use a random device to determine her choice.

Indifference, however, may under some circumstances be a misleading term
because it seems to imply lack of concern and lack of feelings. One may
indeed be indifferent between having fish or steak for dinner, but a
physician who has to allocate a kidney to one rather than another
patient can hardly be characterized as being indifferent. Elster
(1989) proposed to distinguish between situations in which the choice
consequences are insignificant and hence the decision-maker is truly
indifferent and indeterminacy in which the
consequences are highly important but the arguments in both directions
can be judged as equally strong.

Also, from an ethical point of view the use of randomizers is
sometimes recommended, especially in situations where it is important
to ensure an unbiased procedure. Lotteries or lottery-like procedures
have been used not only for deciding who should win the million-dollar
prize, but also for less rewarding outcomes like drafts for military
service, car controls, or in assigning patients blindly to the control
or experimental condition in tests of a novel medical treatment. Such
procedures have the advantage of being perceived as fair, by
giving everybody an equal chance of being selected (Broome,
1984).2 Under such circumstances,
the decision to use a randomizer may be seen justifiable and
based on moral and rational considerations, even if the final outcome
of the decision is due to chance.

1.1  The present studies

In this article we present a series of studies designed to examine the
extent to which the use of a randomizer, such as a coin flip, is
considered as an acceptable decision device. There are at least two
general conditions under which a decision maker may consider the use
of a coin. First, and most important, a coin may be used in situations
of indecision, in particular when the two alternatives are equally
attractive (unattractive) and the relevant attributes are
non-compensatory and can not be directly compared (e.g., Luce, Payne,
& Bettman, 1999). Second, a coin may be contemplated under
circumstances of what Beattie, Baron, Hershey, and Spranca (1994)
termed “decision aversion”, situations in which people prefer to
avoid making decisions. Such situations usually arise when the
consequences of the decisions are of tremendous importance, as for
example determining who among two soldiers will be send on a mission
in which the chance of survival is small. Third, a coin or a similar
lottery procedure might be advocated in situations where it is
important to avoid a biased decision, for instance by a partial or
prejudiced decision maker. Our study investigates whether, and under
what conditions, people are willing to accept the use of a randomizer
in such situations.

Consider the following scenario which, supposedly, most people would
find difficult to cope with, and will probably lead to decision
aversion. A young man and an old lady were involved in a serious car
accident. The police have determined, unequivocally, that it was the
young driver’s fault: He did not comply with a stop sign. The two
victims are brought to hospital in a critical condition. The physician
on duty determines that to save their lives, both have to be placed
immediately in the intensive care unit. Unfortunately, only one unit
is currently available and the physician has to decide which of the
two should be saved. Presumably, the arguments in favor of saving each
of the two victims are equally strong. On one hand, the accident has
been caused by negligence of the young man, suggesting that the old
lady should be saved. On the other hand, the life expectancy of the
old lady is much shorter, suggesting that the young man should get the
priority. Which of the two arguments should prevail?

The first experiment tested the extent to which people were willing to
accept the use of a randomizer, more specifically a coin, in a
situation of indeterminacy, using the accident scenario described
above. There were two main conditions. In the judgment
condition, participants judged whether there were stronger reasons for
one of the two options (i.e., saving the young man or saving the old
lady) or whether the reasons were equally strong. In the
choice condition, participants were asked to choose between
the two options or alternatively use a coin to determine their choice.
It was hypothesized that in the judgment condition most participants
would acknowledge the indeterminacy of the situation (i.e., admit the
existence of equally strong reasons supporting one or the other
option). Nonetheless, it was predicted that because of people’s
reluctance to use a randomizer in important decisions (involving life
and death), few participants would accept the use of a coin. In other
words, we expect in these situations a discrepancy between people’s
judgments and their actual choice decisions.

In the subsequent experiments, we tested several variations over the
same theme. To make sure that the results of Experiment 1 were not due
to peculiarities of the young-man/old-lady scenario, a kidney
allocation scenario, which perhaps could claim a higher degree of
realism, was introduced in Experiment 3. In successive experiments, we
tested the following factors that could possibly affect people’s
willingness to use a coin in situations of indeterminacy, namely (1)
seriousness of outcome; (2) focus on indeterminacy; (3) focus on
fairness; and (4) the nature of the randomizer.

(1) People may find it especially problematic to use a coin flip to
decide serious outcomes, like matters of life or death, even in
situations they admit to be indeterminate, resulting in high
judgment-decision discrepancies. In situations of less
importance, we expect people to be more willing to accept random
procedures as a decision aid. In such situations we predict the
judgment-decision discrepancy to be reduced or even to disappear. This
prediction is tested in Experiment 4. Using a similar logic, one might
think it would be easier to use a randomizer when the outcome is not
categorical (life or death), but probabilistic (a smaller or greater
chance of life or death). Probabilistic alternatives are, in a sense,
less severe than deterministic ones; after all, the “losing” patient
in the accident scenario is not condemned to die, but merely to a
reduced chance of survival. This possibility is explored in Experiment
5.

(2) People may decline to use a randomizer in the hope of eventually
finding a more rational solution to the decision problem, even in cases
where they do not see the advantage of one option over the other and
have a hard time making up their mind. Elaborate descriptions that
underscore the indeterminacy of the situation could remove this
possibility, and might accordingly make people more willing to accept a
randomizer as a way out of the impasse. This could be achieved by
casting the decision as a conflict between individual opinions, or
letting them explicitly acknowledge the lack of other solutions. The
effects of such prompts are studied in Experiment 6. Furthermore, an
increase in similarity between the alternatives might make people
realize that there are no compelling reasons for favoring one or the
other option and thus be more amenable to use a randomizer. Thus in
Experiment 7 participants are given a choice between saving two middle-aged
ladies rather than the young-man/old-lady dilemma in our original
scenario. With more similar options, the likelihood of finding a
correct rational solution is reduced, and perhaps also the decision
maker will feel that the outcome makes less of a difference.

(3) A chance device is not only helpful for the decision maker but
also assures other implicated parties against partial or biased
decision making. People might be more favourably disposed towards
chance procedures when focus is directed toward their fairness. This
can be done simply by asking people to indicate not just what are
preferred or acceptable ways of making decisions in case of
indeterminacy, but what is a fair way of doing it. In the
present studies we ask which of three alternatives in the accident
scenario is more fair (Experiment 2), and instruct participants to
rate decisions made by a randomizer for fairness as well as for
acceptability (Experiment 7). In addition, we describe in Experiment
10 a situation where the decision maker may be biased (or suspected of
being biased) towards one of the alternatives. The question we raise
is whether the use of a coin, which may eliminate the suspected bias,
is now acceptable.

(4) Randomness is an intricate concept. Although every one “knows”
what randomness is, it somehow eludes satisfactory definition. As
noted by several authors, randomness lacks both an adequate and
precise definition as well as a satisfactory and decisive test that
will determine its presence (e.g., Falk & Konold, 1997; Pashley,
1993). Moreover, a large body of research has shown that people’s
intuitions of randomness are not always compatible with formal models
(e.g., Bar-Hillel & Wagenaar, 1993; Falk, 1991; Neuringer, 1986). It
is thus not obvious what people are willing to accept as an adequate
random procedure. Such procedures can differ on a concrete level; one
can, for instance draw lots, toss a coin, or pass the decision to
another agent that is supposed not to be biased in any particular
direction. Will such procedures differ in how random they are
perceived and in turn how acceptable, and how fair, they are judged to
be? This is an issue explored in Experiment 8.

Random procedures, however, can also be described at different levels
of abstraction. Vallacher and Wegner (1987) argued in their action
identification theory that an action described on a specific level
(“I am reading an article”) have different connotations from the
same action described at a more general level (“I am studying”).
Problematic procedures are typically described on a more detailed
level than smoothly running, routine activities. Analogously,
suggestions about “tossing a coin” might evoke other, and perhaps
more objectionable associations than “using a randomizer”. In
construal level theory, Trope and Liberman (2003) have discussed how
events that are psychologically (for instance temporally) close tend
to be described on a more concrete level than events that are
perceived as more distant. When people focus on far and abstract tasks
they typically focus more on advantages and reasons why they
should be done, whereas immediate prospects draw attention to
procedural details, with a primary concern for how they
should be performed. As a result, a task or a procedure described on
low levels of construal will often result in more negative evaluations
than the same task construed at a higher, more general
level. Experiment 9 was designed to test the acceptability of random
procedures described at different levels of construal, to test whether
the acceptability of chance in principle is similar or
different from the acceptability of using a concrete randomizer like
the coin.

2  Experiment 1

Experiment 1: Accident scenario
 

(a) Old Lady

This Post: Decisions by coin toss: Inappropriate but fair

(b) Young man

(c) Equality*

N

Judgment

10 (16.4%)

15 (24.6%)

36 (59.0%)

61

Choice

17 (29.3%)

31 (53.4%)

10 (17.2%)

58

Experiment 2: Accident scenario (Fairness)
 

(a) Old Lady

This Post: Decisions by coin toss: Inappropriate but fair

(b) Young man

(c) Equality

N

Judgment

4 (8.9%)

7 (15.6%)

34 (75.6%)

45

Choice

10 (22.2%)

19 (42.2%)

16 (35.6%)

45

Experiment 3: Kidney transplantation scenario
 

(a) Robert

(b) John

(c) Equality

N

Judgment

23 (30.3%)

13 (17.1%)

40 (52.6%)

76

Choice

34 (44.7%)

22 (28.9%)

20 (26.3%)

76

* Equality implies flip of a
coin in the choice condition and judging the arguments being equally
persuasive in the judgment condition.

Participants. A total of 119 undergraduate students were
recruited at the campus of Eindhoven University of Technology and were
asked to participate in a task that lasted for a few minutes. They
received a chocolate bar for their participation.

Design and procedure. All participants were presented with
the following scenario:

Dr. Freedman and Dr. Peterson were both on duty in the
emergency room when the ambulance arrived with two critical injures, an
old lady aged 69 and a young man aged 32. They were injured in an
accident, caused by a collision between their two cars. The police has
determined, unequivocally, that it was the young man’s
fault — evidently, the lady had the right of way. The two physicians
agree that, in order to save their lives, both the old lady and the
young man have to be placed immediately in an intensive care unit.
Unfortunately, the hospital is a small one and currently there is only
one intensive care unit free. The two physicians are faced with the
problem of whom should they place in the intensive care unit: The old
lady or the young man? They both realize that this difficult decision
needs to be made very quickly.

Dr. Freedman believes that the old lady should get priority because
the accident was caused by the young man’s fault. Dr. Peterson
believes that the young man should get priority because his life
expectancy is obviously much larger. They are uncertain as to what to
do, and quickly consult a third physician who happened to be near by.

Participants In the judgment condition were further told: “This
physician holds that both arguments are equally valid and equally
strong.”

Participants in the choice condition were further told:
“This physician holds that both arguments are equally
valid and equally strong. Hence, he believes that the best way to solve
the dilemma is simply by using a coin flip.”

The experiment consisted of two conditions. Participants in the
judgment condition were asked to indicate with whom of the three
physicians they most agreed. Their task was to judge whether the
arguments were more valid and weighed heavier in favor of (a) saving
the old lady, (b) saving the young man, or (c) both arguments were
equally valid and of equal weight. Participants in the choice condition
were asked to decide which of the following would be the most
appropriate action: (a) save the old lady’s life, (b)
save the young man’s life, or (c) make the decision by
the flip of a coin. The scenario was constructed such that the
arguments for options (a) and (b) would be assessed as equally
appealing, and hence it was expected that a large number of
participants in the judgment condition would opt for option (c).
Following the above discussion, however, it was predicted that in the
choice condition, the corresponding option (c), namely the flip of a
coin, would not be endorsed by most participants.

2.2  Results and discussion

In both conditions of this experiment, as in the various conditions of
the following experiments, the order of arguments for both choice
options, (e.g., in the present scenario, the arguments for saving
either the old lady or the young man), were counterbalanced. In all
experiments, no systematic differences due to the order of presenting
the arguments were found. Consequently, in all the analyses below the
data were combined across order presentations.

The results are portrayed in the upper part of Table 1. The frequencies
for options (a) and (b) were combined and compared to the frequency of
option (c). As predicted, a majority of participants in the judgment
condition (36 of 61, or 59.0%) judged the arguments for both options
to be equally compelling, i.e., carrying equally strong weights. In
contrast, only a minority in the choice condition (10 out of 58, or
17.2%) considered the corresponding option of using the coin to be the
most appropriate action. The difference between the two proportions is
highly significant (z=4.68; p<.001). Evidently, although the
two options were judged to be equally (un)attractive, it does not
justify the use of a coin. One possible explanation for this
judgment-choice discrepancy is that choice, unlike judgment,
implies commitment (e.g., Ganzach 1995), and participants refuse to
make such a commitment based on a coin flip.

3  Experiment 2

Coin tosses and random draws have been used in situations of
indeterminacy not only to break ties but also to make sure that the
decisions are unbiased and not (consciously or unconsciously)
influenced by irrelevant sympathies or prejudices on the part of the
decision maker. Random procedures can be considered fair in the sense
that none of the options are given an advantage over the other.
Experiment 2 was conducted to investigate whether a focus on fairness
would make participants more favourably disposed towards decision by
coin toss. The same scenario as in Experiment 1 was employed, except
that this time participants were asked to make their choice and
judgment decisions on the basis of fairness (rather than on the basis
of what is more appropriate).

Participants. A total of 90 undergraduate students were
recruited at the campus of the Pabo College in Eindhoven, and were
asked to participate in a task which lasted a few minutes. They were
randomly assigned to the choice (N=45) or the judgment
(N=45) task.

Design and procedure. The experiment was identical to
Experiment 1, except that participants receiving the judgment task were
asked to judge whether the arguments for saving the old lady were most
fair, the arguments for saving the young man were most fair, or that
the arguments for the two protagonists were equally fair. Similarly,
participants in the choice task, were asked to decide which of the
three choice decisions — saving the old lady, saving the young man or,
flipping a coin — was the most fair one.

3.2  Results and discussion

As shown in the middle panel of Table 1, a majority (75.6%) of the
participants in the judgment task considered the arguments to be
equally fair. In contrast, a significantly smaller proportion (35.6%)
of participants in the choice task considered it most fair to use a
randomizer. Apparently, although most participants in the judgment
condition tend to agree that the arguments in support of each of the
two protagonists are equally fair, only a minority in the choice
condition accepts the coin flip as a fair solution. Evidently, the
aversion to using random devices for resolving a conflict is deeply
rooted. The pattern of results of Experiment 2 is highly similar to
that obtained in Experiment 1. Comparing the results of Experiment 1
and 2 using a Breslow-Day homogeneity of odds ratios test (Agresti,
1996) yielded a non-significant result (χ2 =
.109; p = .74).

Fairness can be thought of in two distinct ways. One, usually referred
to as distribution (allocation) fairness, involves
equal sharing. Thus dividing $100 fairly among two persons would
imply that each one gets $50. In the above scenario, it would entail
that since the arguments for saving either the old lady or the young
man are perceived as equally strong, both should get equal
opportunities (chances) of survival. A second interpretation of
fairness (which does not contrast the previous one), concerns the
process by which the decision has been made. For instance, consider
two sisters who inherited an old family piano. One may believe that
deciding who of the two sisters should get the piano by asking a
neutral judge is a more fair procedure than tossing a coin. Fairness
in the present context seems to be more related to process fairness, a
point on which we further comment in the discussion of Experiment 9.

4  Experiment 3

The main characteristics of the accident scenario, employed in
Experiment 1 and 2, are the importance of the outcomes (life or death),
the irreversibility of the decision, the lack of any compelling
normative considerations that could tilt the decision in one or the
other direction, and the urgency to reach a decision fast required by
the situation (procrastination would lead to the worse outcome namely
both victims will die). To obtain further generality, the main results
were tested using a different scenario with similar characteristics,
which may be perceived as being perhaps more realistic than the
accident scenario. Specifically, a scenario was employed in which a
decision had to be made as to who, among two patients, will receive the
only kidney available. The situation of indeterminacy was achieved by
the fact that one patient was younger and thus had a longer life
expectancy while the other had, according to the physicians, a higher
chance of a successful transplantation.

Participants. A total of 152 undergraduate students,
recruited at the campuses of the university of Nijmegen participated
in the experiment. They performed the task on a computer (laptop),
along with several unrelated judgmental tasks, and were paid €5.50
(approximately $7.00 at the time the experiment was conducted) for
their participation.

Design and procedure. All participants were exposed to the
following scenario:

John and Robert are two patients waiting urgently for kidney
transplantation. The hospital just received a kidney that matches the
requirements of the two patients. The physicians responsible for the
transplantation are facing a difficult decision, namely to whom they
should allocate the kidney. On one hand John, aged 50, is younger than
Robert, aged 57. On the other hand, Robert’s condition
is better and the three physicians believe that he has an 85% chance
that the transplantation will be successful compared with John whose
chance for a successful transplantation they assess as 75%. As you
may note, John has a slightly higher life expectancy. On the other
hand, Robert has a slightly higher chance for a successful operation.

– Physician A thinks that the kidney should be given to John because,
given that the transplantation is successful, he has a longer life
expectancy compared to Robert.

– Physician B believes that the kidney should be given to Robert
because he has a higher chance for a successful transplantation than
John.

– Physician C believes that the arguments to allot the kidney to John
are equally strong and equally convincing as the arguments to allot the
Kidney to Robert.

Participants in the judgment condition were further asked:

If you had to judge, which of the following options would you most agree
with:

– The arguments to allot the kidney to John, who has a longer life
expectancy, are more compelling.

– The arguments to allot the kidney to Robert, whose chance for a
successful transplantation is higher, are more compelling.

– The arguments to allot the kidney to one or the other patient are
equally strong and equally compelling.

Participants in the choice condition were further asked:

If you had to make the choice, which of the following options would you
choose.

– Allot the kidney to John, who has a longer life expectancy.

– Allot the kidney to Robert, whose chance for a successful
transplantation is higher.

– Toss a coin to decide to whom to allot the kidney because the
arguments in favor of the two patients are equally compelling.

In both conditions, the equality (coin toss) option was in the third
place, and the first two options (regarding Robert and John) were
counterbalanced.

The results are portrayed in the lower part of Table 1. As can be
seen, there was a slight preference, in both the judgment and choice
conditions, in favor of Robert (the patient who had a higher chance
for a successful operation). Hence, we did not achieve complete
indeterminacy. Notwithstanding, and more important, there was as
expected a substantial and statistically significant difference
(z=3.30; p < .001) between the proportion
of participants who judged the reasons for allocating the kidney to
one or the other patient as being equally convincing (53%), and the
corresponding number of participants in the choice condition who opted
for the coin toss (26%). These results further demonstrate the deep
rooted aversion that people posses regarding the use of a coin as an
acceptable decision device for solving complex and important decision
problems.

5  Experiment 4

Do the above results generalize also to situations in which the
consequences are less imperative, and the question is not one of life
or death? Experiment 4 was designed to test Elster’s (1989)
hypothesis concerning the distinction between indifference
and indeterminacy. Specifically, as in Experiments 1–3,
participants were allocated to either the judgment or the choice
conditions. Two scenarios (between subjects) were used; one with
“medium” important consequences (first authorship of an article) and
one with “low” important consequences (whether to attend a theater
play or a concert). It was predicted that, when decision consequences
are of minor importance, participants would be less reluctant to use
the coin.

1. First author scenario
 

(a) John

(b) Peter

(c) Equality

N

Judgment

11 (17.2%)

26 (40.6%)

27 (42.2%)

64

Choice

16 (25.4%)

28 (44.4%)

19 (30.2%)

63

2. Entertainment scenario
 

(a) Theater

(b) Concert

(c) Equality

N

Judgment

7 (9.0%)

38 (48.7%)

33 (42.3%)

78

Choice

8 (9.9%)

31 (38.3%)

42 (51.9%)

81

Participants. A total of 286 undergraduate students, recruited
at the campuses of Nijmegen University and the Free University of
Amsterdam, participated in this and other, unrelated decision-making
tasks, for which they were paid an equivalent of approximately $5.00.

Design and procedure. Participants from Nijmegen University
(N=127) were exposed to the “first author” scenario (medium
consequences), and were randomly assigned to the choice or the
judgment task. They were presented with the following cover story.

John and Peter have written a short article for a
computer science journal. The article was praised by the editor as
original and well written and was accepted for publication. Before
sending the final version for print, the two authors have an argument
regarding the order of the authors’ names. John claims
that he was the one that came up with the original idea and therefore
his name should appear first. Peter claims that he was the one that has
actually written the article and has done most of the work, and thus
his name should appear first. They are uncertain as to what to do, and
quickly consult a friend who happened to be nearby.

Participants in the judgment condition were further told:
“The friend thinks that both arguments are equally valid
and equally strong.”

Participants in the choice condition were further told: “The
friend thinks that both arguments are equally valid and equally
strong. Hence, he believes that the best way to solve the dilemma is
simply by using a coin flip.”

Participants from the University of Amsterdam (N=159) were
exposed to the “choice of entertainment” scenario, and were randomly
assigned to the choice or judgment task. They were presented with the
following cover story.

Both Richard and Brad have just obtained their driving
license. They want to celebrate the event with an evening of
entertainment. On the evening that suits them both, a play is performed
at the theater and a jazz concert is given at the music hall. The two
friends find it difficult to choose. The play will be performed by a
very good theater company, and they are both fond of the music that
will be played at the concert.

Richard suggests to go to the theater. The theater is much easier to
reach than the music hall. Also, he has not seen the auditorium since
its recent renovation. Brad suggests to go to the concert. The music
hall is situated far out of the city centre, but next to it is a nice
restaurant where they could go and have dinner before the show.
Besides, he loves the music hall’s cozy atmosphere. They are
uncertain as to what to do and quickly consult a friend who happens to
be nearby.

Participants in the judgment condition were further told:
“Their friend thinks that both arguments are equally valid and equally
strong.”

Participants in the choice condition were further told:
“Their friend thinks that both arguments are equally valid and equally
strong. Hence, he believes that the best way to solve the dilemma is
simply by using a coin flip.”

As in the previous experiments, participants in the judgment task were
asked to judge for which option (John or Peter in the first scenario;
theater or concert in the second scenario) there were more compelling
reasons or, as third alternative, whether the reasons for the two
options were equally compelling. Participants in the choice condition
had to choose one of the two options or opt for a coin flip.

5.2  Results and discussion

The results are portrayed in Table 2. In the authorship scenario (mild
consequences), the proportion of participants in the judgment task that
considered the arguments to be equally strong (27 out of 64, or
42.2%), was larger but did not differ significantly from the
proportion of participants in the choice task (19 out of 63, or 30.2%)
that considered the use of a randomizer to be appropriate. In the
choice of entertainment scenario (unimportant consequences), there
seemed to be a clear preference for the concert over the theater. More
important, however, the proportion of participants that judged the
arguments for the two events to be equally forceful (33 of 78, or
42.3%) did not differ significantly from the corresponding proportion
in the choice task that considered the use of a randomizer appropriate
(51.9%). Further, we compared the proportion of participants who
accepted the coin in the choice conditions of the three different
scenarios of Experiments 1 and 3. Using the Cochran Armitage test
(Agresti, 1996) indicated a significant trend (z=4.28;
p <.001) in which the proportion of participants
accepting the use of a coin was the smallest in Experiment 1, larger
for the first author scenario, and even larger for the choice of
entertainment scenario.

In sum, the pattern of responses to the choice and judgment conditions
differed significantly only in the case of severe consequence
(Experiments 1–3), as opposed to situations where the consequences were
relatively unimportant (Experiment 4). Participants were less reluctant
to accept a randomizer in cases where they were indifferent, whereas
they preferred to make a choice in a situation of indeterminacy.

 

(a) Old lady

(b) Young man

(c) Coin toss

N

Deterministic choice

13 (29%)

18 (40%)

14 (31%)

45

Probabilistic choice

13 (29%)

19 (42%)

13 (29%)

45

6  Experiment 5

Experiment 5 asked whether a concrete random procedure (such as coin
toss) is more acceptable in a situation where the outcome itself is
uncertain. In the original version of the old-lady/young-man
scenario, the coin toss literally determined life and death for the
patients involved. It may be considered less “callous” to let the
coin decide upon treatment priorities, condemning none of the victims
to a sure death, but use it for allocating them to two treatment
facilities with different chances of survival. In the present
experiment the coin gave both patients a chance of being saved, but
with different probabilities.

Participants. A total of 90 undergraduate students were
recruited at the campus of the Pabo College in Eindhoven. They
performed the task on a computer (laptop), along with several unrelated
judgmental tasks, and were paid €4.00 (approximately $5.00) for
their participation.

Design and procedure. All participants were exposed to the
basic scenario employed in Experiment 1. They were randomly allocated
to one of two conditions. One condition (deterministic choice) was an
exact replication of the choice condition of Experiment 1. The other
condition was very similar except that participants in this condition
were told that the hospital had two (rather than one) intensive care
units. The two units, however, were not identical: One was a modern
newly purchased unit while the other one was an old model, purchased 25
years ago, that lacked several of the new model features. The
physicians estimated that whoever (of the two injured) is going to be
placed in the new unit, has an 80% survival chance. They further
estimated that whoever (of the two injured) is going to be placed in
the old unit, has a 40% chance to survive.

As in the choice condition of Experiment 1, participants in both
conditions had to choose one of three alternatives (save the young man,
save the old lady, or toss a coin).

6.2  Results and discussion

The results are portrayed in Table 3. The percentage of participants who
chose the coin toss is almost the same in both conditions, and is not
different from the comparable percentage in the choice condition of
Experiment 1. The results serve as yet another replication of the
reluctance to use the coin. Further, the phenomenon is robust and is
equally strong also under probabilistic conditions, namely when the
decision does not unequivocally determine life and death. Thus, even
if less important decisions allow for the use of a coin, as
demonstrated in the previous experiment, the present attempt to reduce
the severity of the accident scenario (by varying probabilities rather
than outcomes) was not successful in making a randomizer more
acceptable.

7  Experiment 6

Reluctance to use a randomizer could be due to a hope of finding a
better and more rational solution. In other words, participants may
believe that the situation is not completely indeterminate after all,
and that a reason-based solution may be found out of the impasse. The
following two experiments examine the effects of emphasizing the
indeterminacy of the situation, and in this way attempt to weaken one
source of resistance to the coin. In Experiment 6, this is done in one
condition by making it clear that none of the physicians is going to
be swayed by the other’s argument, an in another condition by
explicitly pointing out the lack of an alternative procedure.

 

(a) Old Lady

This Post: Decisions by coin toss: Inappropriate but fair

(b) Young man

(c) Equality

N

I. Control Condition

Judgment

12 (19.7%)

12 (19.7%)

37 (60.6%)

61

Choice

20 (35.7%)

23 (41.1%)

13 (23.2%)

56

2. Conflict Condition

Judgment

5 ( 9.4%)

10 (18.8%)

38 (71.7%)

53

Choice

13 (27.1%)

12 (25.0%)

23 (47.9%)

48

3. No better option

Judgment

11 (22.5%)

10 (20.4%)

28 (57.1%)

49

Choice

16 (34.0%)

12 (25.5%)

19 (40.5%)

47

Participants. A total of 314 undergraduate students,
recruited at the campuses of the universities of Tilburg, Nijmegen, and
Utrecht participated in the experiment. They performed the task on a
computer (laptop), along with several unrelated judgmental tasks, and
were paid €5.50 (approximately $6.50 at the time the experiment
was conducted) for their participation.

Design and procedure. Participants in this experiment were
presented with a very similar version of the cover story employed in
Experiment 1. They were allocated to one of three conditions. In each
condition, half of the participants were assigned to the judgment and
the other half to the choice task. The original condition was
an exact replication of Experiment 1 except that the old lady’s age
was changed from 69 to 59 years, because preceding results had shown
that among participants who were not indeterminate (in either the
choice or the judgment condition), there was a slight tendency to
prefer saving the young man. Participants in the conflict
condition read the same cover story with the addition that the
disagreement among the two physicians was emphasized by noting that
the two were very strong-minded about their own preference (implicitly
suggesting a conflict that leads to an impasse). In the no
better option condition, the scenario was again the same except
that the third physician drew the attention of the other two
physicians to the question whether there were any better choice
alternatives to the use of a randomizer. The experiment thus consisted
of a 3 (Original, Conflict, and No better option conditions) X 2
(judgment vs. choice) between-subjects design.

7.2  Results and discussion

Table 4 shows that overall, participants who chose either the old
lady or the young man were about equally distributed over the two
options, indicating that participants, as a group, did not have a clear
preference for either one of the two options. As before, the focus of
interest is on the distribution of responses over the randomizer versus
choosing one of the options, i.e., the old lady or the young man, data
were collapsed over the latter two for further analysis.

Results in the original condition replicated earlier
findings. A majority (61%) of the participants in the judgment
condition considered the arguments for saving the old lady or the
young man as equally strong. In contrast, less than one fourth (23%)
of the participants in the choice condition considered the
use of a coin to make a decision as appropriate. As in Experiment 1,
the proportion of participants in the judgment condition assessing the
arguments to be equally strong was significantly larger than the
corresponding proportion in the choice condition who assessed the coin
to be acceptable (z = 4.09; p < .0001).
These results again show people’s reluctance to use a coin in a
situation of indeterminacy.

In the conflict condition, again a majority (72%) of
participants in the judgment condition considered the arguments for
saving the old lady or the young man as equally strong. About half
(48%) of the participants in the choice condition were willing to use
a coin to make a decision. The proportion of participants accepting the
coin in the judgment condition was significantly larger than the
corresponding proportion in the choice condition (z = 2.44;
p < .001), though the effect size was smaller than
in the original condition.

Finally, in the no better option condition, a small majority
(57%) of participants in the judgment condition considered the
arguments for saving the old lady or the young man as equally strong,
yet less than (40%) of the participants in the choice condition were
willing to use a coin to make a decision. The difference was in the
same direction as in the other two condition, yet (close to but) not
statistically significant (z = 1.63; p = .052).

Examining only participants who had to make an explicit choice, we
tested whether the proportion who accepted the coin as an appropriate
choice procedure, was larger in the conflict and best
option condition compared with the original (base line) condition.
Indeed, the proportion of participants who accepted the coin was much
larger in the conflict condition than in the original condition (47.9%
vs. 23.2%). This difference was statistically significant (z
= 2.64, p < .005). The proportion of participants
who accepted the coin in the best option condition (40.4%) was also
significantly larger (z = 1.88; p < .05)
than in the original condition.

Evidently, highlighting the conflict and suggesting that perhaps
there are no other alternatives to the use of a randomizer, elevated
the number of participants who accepted the coin as a suitable choice
procedure. Notwithstanding, in both of these latter conditions, there
was a clear gap between the proportion who judged the arguments to
carry equal weights and the corresponding proportion of participants
who accepted the coin as a proper decision device. Further, although
the objection to the use of a coin was mitigated in the two conditions,
nonetheless more than 50% still refused to endorse the coin.

In the present experiment an attempt was made to reduce the
resistance to the use of the coin by pointing out the lack of a better
alternative. Yet, participants may still assume, even if erroneously,
that by investing adequate effort one may find sufficient reasons to
justify one or the other option. What would happen, however, if the two
alternative options were made so similar that no sensible reasons would
exist that can justify the choice of one option over the other. For
instance, would a coin be more acceptable if the accident victims were
two middle aged women (so that they are, as far as the physician is
concerned, equal on all relevant dimensions). The following experiment
was designed to test this possibility.

 AcceptanceFairness
 

n

Mean (S.D)

n

Mean (S.D.)

First rating (separate)

1. Young man vs. old lady

35

3.31 (3.34)

37

2.84 (3.23)

2. Two middle aged ladies

37

3.03 (3.30)

35

3.51 (3.19)

Second rating (joint)

1. Young man vs. old lady

37

1.70 (1.87)

35

1.74 (2.16)

2. Two middle aged ladies

35

5.51 (3.71)

37

5.32 (3.76)

8  Experiment 7

Participants. A total of 144 undergraduate students,
recruited at the campus of Tilburg University participated in the
experiment. They performed the task on a computer (laptop), along with
several unrelated judgmental tasks, and were paid €5.00
(approximately $6.50) for their participation.

Design and procedure. Participants were exposed to two
versions of the cover story employed in Experiment 1, presented
separately, one after the other, on two different screens. One was the
same cover story as employed in Experiment 1 except that the third
physician (who was supposed to break the tie) was omitted. The other
cover story was the same except that the young man and the old lady
were replaced by two middle aged women, and no mention was made as to
who was responsible for the accident. Hence, in this condition, it was
impossible to come up with reasons that would favor one of the victims
more than the other. At the end of each cover story, participants were
told that the two physicians find it extremely difficult to decide
which of the two victims to save and, due to the time pressure, decide
to use a coin. Half of the participants were asked, (after each
story separately) to judge on a 0–10 scale to what extent they
thought the use of the coin was an acceptable decision
procedure (0 completely unacceptable; 10 completely acceptable). The
other half had to rate, on a similar scale, the fairness of
the use of a coin (0 completely unfair; 10 completely fair). Within
each of these two conditions (judgment of acceptability or fairness),
the order of presenting the two scenarios was counter-balanced: Half
of the participants in each condition were first exposed to the
original (old-lady/young-man) cover story and after rating it were
exposed to the two middle-aged women scenario. The other half received
the two scenarios in a reversed order.

It is important to note that, regardless of whether participants
judged the coin acceptability or fairness, the first and second ratings
were essentially different. Specifically, the ratings of the scenario
presented first (either the old-lady/young-man or the two middle aged
ladies) constitutes what Hsee (1996; Hsee, Loewenstein, Blount, &
Bazerman, 1999) has termed separate ratings. Participants in
this case are not yet familiar with the following scenario, and thus
are unable to compare the two scenarios. When exposed to the second
scenario, they are already familiar with the previous scenario which,
in some respects, can serve as a reference point. Hence, the ratings on
the second scenario can be conducted comparatively to the former
ratings, a condition termed by Hsee as joint ratings.

8.2  Results and discussion

The results are portrayed in Table 5. The acceptability and fairness
judgments were analyzed apart, and within each condition the first
(separate) and second (joint) ratings, were also analyzed apart. Each
analysis consists of a simple comparison based on an independent
t-test.

Separate ratings. There was no reliable difference in rating
coin acceptability for the old lady/ young man (M = 3.31) and
the two middle aged ladies (M = 3.03) scenarios (t =
.367; p > .70). Similarly, for the coin fairness
ratings there was no reliable difference between the
old-lady/young-man (M = 2.84) and the two middle aged ladies
(M = 3.51) scenarios (t = .894; p
> .37). It thus seems that participants did not
distinguish between these two scenarios — use of the coin received a
rather low rating on both the acceptability and the fairness scale for
both scenarios.

Joint ratings. Coin acceptability was rated much higher in
the two middle aged ladies (M = 5.51) compared with the old
lady/young man (M = 1.70) scenario, a difference that was
highly significant (t = 5.56; p < .0001). A
similar difference was also observed for the coin fairness judgments:
Fairness ratings of the middle aged ladies scenario (M = 5.32)
was much larger than the comparable rating for the old-lady/young-man
scenario (M = 1.74), a difference that was statistically
reliable (t = 4.91; p < .0001).

Two main conclusions can be drawn from these results. First, in the
separate presentation mode, when viewed in isolation (supposedly, the
more likely situation), the coin is equally rejected (and judged
unfair) for both scenarios. The fact that in the two middle aged
ladies scenario, given the information, there are no possible reasons
to prefer one over the other did not reduce the aversion to using a
coin. Second, there is a large difference in acceptability of the
coin in the case of the second ratings which, supposedly are compared
with the first ratings. Under such a comparative condition, the first
rating provides a reference point to which the second can be compared.
Participants’ attention is thus directed to the difference between the
two scenarios. Indeed, under these conditions the aversion to using
the coin in the two middle age ladies scenario is drastically
reduced. Nonetheless, it should be noticed that even in this case, the
acceptability and fairness of the coin do not significantly exceed the
middle (5.5) scale value. Evidently, the dislike of using a coin for
vital decisions is deeply rooted, even when no reason exists for
preferring one option to another.

9  Experiment 8

 

N

Old Lady

Young man

Equality

Decision — Coin

40

10

18

12 (30%)

Decision — Random device

36

7

5

24 (67%)

Decision — Same chance

37

4

4

29 (78%)

Judgment — Reasons

39

3

10

26 (67%)

In all the preceding experiments, the coin has been used to represent
a prototypical chance device. However, there may be features of this
specific randomizer that makes it an unwanted tie breaker, at least in
a medical scenario which supposedly is about saving lives and not
about gambling. The present experiment was designed to investigate
whether the manner in which the randomizer is described will influence
its degree of acceptability. A coin toss belongs to a more general
category of randomizers and can alternatively be called “a random
device” or a procedure that offers “equal chances” to the parties
involved. Such more general or more abstract descriptors may distract
people’s attention away from particular unattractive properties of the
coin and ask for their endorsement of the principles involved rather
than their attitudes toward one particular instantiation of these
principles.

Participants. A total of 152 students, recruited from a
pool of participants (from different Dutch universities) who registered
for taking part in ongoing experiments via e-mail, participated in the
experiment. They were paid for this as well as other experiment at the
rate of €1 per experiment.

Design and procedure. All participants were exposed to the
basic scenario employed in Experiment 1. The scenario ended by
informing participants that one of the physicians thought the old lady
should be saved because the accident was not caused by her whereas the
other physician thought the young man should be saved because he had a
longer life expectancy. Participants were further assigned to four
different conditions, three that involved a choice decision and one
that involved judgment. Participants in the Coin condition
were asked the following: Suppose you had to make a choice. Would you
(i) save the old lady, (ii) save the young man, and (iii) toss a coin
to determine who should be saved. This condition is in fact a
replication of the corresponding condition in Experiment 1.
Participants in the Random device condition were exposed to
the same choice decision except that the third option was formulated
as “use a random device to determine who should be
saved.” The purpose of this manipulation was to test
whether people reject any random procedure or whether their objection
is more directed toward the use of the specific random device, namely
the coin. For participants in the Equal Chance condition, the
third choice option was “give an equal chance for saving either of
the two victims.” The term “equal chance” is even more
abstract than a random device; moreover, it directs attention towards
the purpose of the selection procedure, rather than to the actual
process or procedure being used. Finally, participants in the
Judgment condition had to judge whether there were stronger
reasons to save (i) the old lady, (ii) the young man, or whether (iii)
the reasons to save each of the two were equally strong. This is a
replication of the corresponding condition in Experiment 1. In each
condition, the order of the first two options (i.e., old lady and
young man) was counterbalanced.

9.2  Results and discussion

The results are shown in Table 6. As can be seen, the coin
condition is the only one in which the majority is opposed to the use
of a randomizer, namely the coin. Evidently, only 30% find the coin
procedure acceptable. In contrast, when the procedure is described in
more abstract terms, namely using a random device or granting the two
victims equal chance, the majority (67% and 78% in the two
conditions, respectively) expresses their approval. Finally, 67% of
the participants in the judgment condition believe that the reasons to
save each of the two victims are equally strong.

The results in the coin and the judgment conditions replicate those
of Experiment 1. Indeed, the proportion of participants who thought
that there were equally strong reasons for saving each of the two
victims was significantly larger than those accepting the coin in the
coin condition (p < .001 by a Fisher exact test).
Further, the majority of the participants accepted the use of a
randomizer when it was framed in abstract terms as using a randomizer
or giving the two victims an equal chance, yet it was rejected by most
participants when the randomizer was explicitly named as a coin. The
proportion accepting the coin was significantly smaller than either the
abstract randomizer formulation (p = .0014 by a Fisher exact
test) or the equal chance formulation (p = .00002 by a Fisher
exact test). This suggests that participants thought that a random
procedure, that would give equal chance, was acceptable. They detest,
however, the concrete procedure of a coin.

One possible explanation for this finding may be in terms of construal
theory (Trope & Liberman, 2003) according to which we tend to
overemphasize abstract, high-level goals and undermine the concrete,
low-level steps needed to reach them. Thus, participants find the
higher-level, abstract inspiration to obtain fairness appealing and
thus endorse the statements that postulate (in an unspecified way)
“equal chance” and the “use of a random device”. However, when it
comes to the concrete achievement of fairness by throwing a coin, the
potential drawbacks of that action are now at the center of
attention. The shift from the abstract intention to ensure fairness to
actually throw the coin is typical of the difference between thinking
about the distant future and thinking about the near future. Whereas
in the distant future we mainly consider the outcome attractiveness,
in the near future, we think about the feasibility and immediate
consequences of our decisions and actions.

10  Experiment 9

In Experiment 8 the (concrete) coin procedure was generally
rejected, whereas two more abstract formulations were judged to be
quite acceptable. However, the experiment does not allow us to conclude
whether the coin is rejected because of its concreteness, or because of
other potential defects. In Experiment 9 the coin procedure
was compared to three other concrete procedures, the question being to
which extent a coin toss is regarded as a fair and representative
random procedure.

Participants. The experiment was conducted with 242
participants. Ninety-three responded by e-mail and were recruited from
the same pool of participants of Experiment 3 (only participants who
did not take part in the previous experiment were recruited). The
remaining 149 participants were recruited at the campus of the
University of Nijmegen who performed the task on a computer (laptop),
along with several unrelated judgmental tasks, and were paid €5.00
(approximately $ 6.50) for their participation.

Design and procedure. All participants were exposed to the
basic scenario employed in Experiment 1. By the end of the scenario,
participants were told that since the two physicians disagreed as to
whom to save, and because the decision could not be deferred, they
decided to use a random procedure. There were 4 possible methods: (i)
Toss of a coin; (ii) A lottery in which a nurse will blindly choose one
of the names; (iii) Choosing randomly the room number in which the
victim to be saved is located, and (iv) Asking the nurse to make the
decision (which, indirectly, also constitutes a random procedure).

Participants were assigned to one of three conditions. Participants in
the choice condition had to indicate their first and second
preferred choice procedure. Participants in the fairness
condition had to indicate which was the most and second most fair
procedure. Participants in the randomness condition had to
judge which procedure was in their opinion the most and second most
random.

10.2  Results and discussion

 

1st rank

2nd rank

Preferred choice procedure

Coin

28 (35%)

34 (42%)

Lottery

11 (14%)

24 (30%)

Room No.

18 (22%)

17 (21%)

Nurse

24 (29%)

6 (7%)

Fairest procedure

Coin

32 (39%)

20 (25%)

Lottery

13 (16%)

36 (45%)

Room No.

15 (19%)

23 (28%)

Nurse

21 (26%)

2 (2%)

Most random procedure

Coin

41 (51%)

26 (32%)

Lottery

19 (23.%)

36 (45%)

Room No.

13 (16%)

17 (21%)

Nurse

8 (10%)

2 ( 2%)

The numbers of participants in each condition (choice, fairness,
randomness) who ranked each of the four alternatives in the first and
in the second place are portrayed in Table 7. A separate analysis was
conducted for each of the three experimental conditions. Specifically,
for each condition we applied a-priori contrasts to Cochran’s Q test
(Agresti, 1996) comparing the proportion of times the coin flip was
ranked first with the other three procedures, and similarly to the
proportion of times the coin flip was ranked first and second
(combined) compared with the other three procedures.3

In the preferred choice procedure condition, the coin toss was ranked
more often as first than in the other procedures (z = 1.817;
p = .035), and as first and second combined (z =
4.70; p < .0001). In the most fair procedure
condition, the coin toss was ranked more often than the other
procedures as first (z = 3.015; p = .0013), and as
first and second combined (z = 3.614; p <
.001). Finally, in the most random procedure condition, the coin toss
was ranked more often than the other procedures as first (z =
5.324; p < .001), and as first and second combined
(z = 8.33; p < .0001). In short, compared
with other random procedures, the coin was clearly perceived as most
fair and most random and, supposedly, was therefore also considered as
the best procedure. It thus seems that most participants judge the coin
as being the favorite procedure on all the three dimensions. In other
words, conditional on making the choice random, the coin was judged as
constituting the most preferred procedure.

The results of this experiment confirm that coin toss is regarded as a
fair procedure, which is accepted as a better tie breaker than other,
less transparent procedures. It is important to realize, as we already
noted in the introduction, that fairness here relates to
distributional fairness, that is equal allocation of chances. The
reluctance to use a coin, which has been established by the preceding
studies, is thus not attributable to deficiencies in distributional
fairness but rather to a general resistance against any concrete
randomization procedure. Apparently, randomizers do not satisfy the
requirements of procedural fairness, even though participants admit,
on a more abstract level (as demonstrated in Experiment 8), that the
parties should have the same chance.

 

N

Robert

John

Coin Toss

Not familiar

26

6.38 (1.96)

6.50 (1.68)

3.73 (2.98)

Familiar with:
Robert

27

6.15 (1.56)

5.59 (1.93)

6.11 (3.11)

John

28

6.79 (1.85)

6.04 (1.91)

4.97 (3.15)

11  Experiment 10

Are there any conditions, under which the use of a concrete
randomizer, specifically a coin, would be acceptable and thus
considered adequate? As noted in the introduction, and further
demonstrated by several studies in different domains of decision
making, the perception of fairness is playing a central role in the
decision process at both the individual and group level. Fairness,
regardless of how exactly it is defined, is a prerequisite to an
acceptable decision process. Because fairness and evenhandedness
constitute the most prominent attribute of the coin, it is surprising
that in several of the experiments that employed the accident scenario,
participants did not consider the coin as a fair solution
(see especially Experiment 2 and the fairness ratings reported in some
of other experiments). However, it is possible that the coin may become
desirable after all when fairness is explicitly and visibly threatened.
Experiment 10 was designed to test this conjecture.

Participants. Eighty-one participants were recruited from
the same pool of participants of Experiment 3 and 9 (only participants
who did not take part in these previous experiments were recruited).

Design and procedure. Participants were exposed to the same
kidney transplant cover story as in Experiment 3. Because in the
previous experiment Robert (who was older but was said to have a higher
chance of a successful transplantation) was slightly favored over John,
a minor change was introduced, namely Robert’s age was
increased from 57 to 59 in order to make him somewhat less attractive
compared with John. Participants were told that the physician on duty
had three possible choices (allot the kidney to John, allot the kidney
to Robert, or flip a coin) and were asked to rate the acceptability of
each of the three options on a scale from 0 (completely unacceptable)
to 10 (completely acceptable). One group (base-line) was exposed to the
above condition that was in fact a replication of the choice condition
in Experiment 3, except that participants had to rate the three
different choicer alternatives, instead of choosing one of them.
Participants in the other two (experimental) groups received the
treatment as the base-line group except that the latter were given the
following additional information:
“In addition, as it turns out, the physician realizes that he knows
John (Robert) who is a distant family member, in contrast to Robert
(John) who is a complete stranger.”

The only difference between the last two groups was that for one the
physician was acquainted with John whereas for the other he was
acquainted with Robert.

11.2  Results and discussion

The results are portrayed in Table 8. As expected, and compatible
with the results of Experiment 3, in the base-line condition, ratings
of allocating the kidney to either of the two patients (mean ratings
for Robert and John were 6.38 and 6.50, respectively) was significantly
higher (p < .001) compared with the coin toss option
(mean rating of 3.73). In contrast, in the two experimental conditions
there was no difference between the ratings of the allocation options
(to one or the other patients) and tossing the coin. Most important,
mean acceptability of the coin toss in the two experimental conditions
in which the physician was acquainted with one of the patients (mean
acceptability for the two conditions combined was 5.53), was
significantly higher (p < .01) compared with the
base line condition (mean acceptability 3.73). Thus, coin acceptability
is largely increased when it is realized that the physician is unlikely
to make an unbiased and fair decision.

Experiment 10 deliberately introduced a factor that explicitly
violated the prerequisite of fairness. Under such conditions the coin
(and probably other randomizers as well) is considered as an acceptable
decision device. Note that the alternative option, namely a rational
reason-based decision is unviable. Evidently, acquaintance of the
physician (the decision maker) with one of the patients introduces a
bias that cannot be repaired.4 It is in
this condition, where it is realized that a decision that would be both
rational and fair is impossible, that the use of the coin is more
appealing. Notwithstanding, it is remarkable that, despite the
successful manipulation in this experiment, the endorsement of the coin
remains limited and its average rating only slightly exceeds the
midpoint acceptability of .5. The entrenched dislike for the coin seems
not to be entirely eradicated.

12  General discussion

The present paper demonstrated a deeply rooted aversion to the use of a
coin as a decision device, in particular when the consequences are of
high importance carrying a high weight. The dislike of the coin has two
facets: First, even when people judge the reasons for the two options
to be equally convincing and carry equal weights, they nevertheless
refuse to choose the coin as a tie breaker, a finding referred to as
judgment-choice inconsistency. Second, the proportions of participants
who accepted the coin were low in absolute terms (usually not exceeding
30%). The phenomenon has been replicated in several experiments using
two different cover stories. In both narratives, most participants
judged the reasons for favoring one or the other protagonist (the old
lady or young man in the accident scenario; one or the other patient in
the kidney scenario) as equally compelling, yet the majority of
participants in the actual choice condition refused to use a coin. The
(combined) consistent experimental evidence leaves little doubt about
the robustness of our findings.

In the introduction, we sketched four sets of circumstances that might
affect people’s willingness to use a randomizer. First, outcome
seriousness. We found, as expected, less reluctance to use a coin in
scenarios with mild to moderate consequences. In Experiment 4 the
decision to use a coin for deciding disputes of authorship and choice
of entertainment was approved by about the same number of participants
as those who found the arguments for both positions equally
persuasive. Thus in these cases no judgment-decision discrepancies was
observed. However, introducing a probabilistic element in the accident
scenario did not make the coin more acceptable (Experiment 5). Issues
of life and death involve, even in the probabilistic case, what Baron
and Spranca (1987) have termed “protected values”. These are values
linked to absolute moral obligations, they display tradeoff
resistance, making compromises and informed decisions difficult. It is
likely that random procedures are especially objectionable in areas
where such sacred or protected values are involved — unless, of
course, one is willing to consider the outcome of a chance event as a
way of expressing the will of God (Elster, 1989; Ekeland, 1991).

Second, we suggested that randomizers might be easier to approve in
cases where the indeterminacy of the situation is being emphasized and
more rational solutions are ruled out. Experiment 6 showed that, when
the dilemma is explicitly acknowledged, more participants are willing
to use a coin. In Experiment 7, participants rated a random decision
between similar victims more acceptable than a random choice between
dissimilar victims, like in the original accident scenario. However,
this difference emerged only in the joint condition, where participants
were able to compare the two situations. Moreover, in both experiments,
the acceptance of the coin remained generally low. Thus indeterminacy
seems to be a necessary, but not a sufficient condition for approving
decisions by chance.

Third, we explored how fair people perceive decisions by
coin. To this question the experiments provide us with a seemingly
puzzling set of answers. A coin flip, according to participants in
Experiment 9, is the most fair of all the random procedures suggested
(Table 7). Yet, life and death decisions by coin are absolutely not
fair. When participants are explicitly asked what is a most fair
decision (Experiment 2), or to rate the fairness of decisions by coin
(Experiment 7), the emphasis on fairness does not make the coin more
acceptable. Evidently, participants are caught in a conflict between
distributional fairness (which the coin clearly satisfies, accounting
for its high acceptability in Experiment 9), and procedural fairness
which the coin does not fulfill as indicated by the results of the two
main scenarios we employed in several experiments. The rejection of the
coin in these experiments suggests that its rejection on grounds of
procedural fairness outweighs its attractiveness in terms of
distributional fairness. Failure of distributional fairness necessarily
implies failure of procedural fairness but the reverse does not
necessarily hold.

It is worthwhile to note that aversion to the use of a randomizer
remains even when issues regarding distributional fairness are omitted.
A recent (yet unpublished) experiment further supports the above
analysis. In this experiment, a scenario was employed regarding a
cancer patient, in which the physician is contemplating between two
alternative treatments. After carefully weighing the pros and cons of
the two treatments, the physician is unable to decide and consequently
employs a coin. Note that in this case there is a single patient and
thus distributional fairness is irrelevant. Compatible with our
previous experiments, results of this experiment show yet again a
profound aversion to the use of a coin, a dislike that cannot be
attributed to distributional fairness.

Although procedural fairness is most likely the major factor
underlying the aversion to the use of randomizers, distributional
fairness may also play a pivotal role under certain circumstances as
exemplified in Experiment 10. In contrast to the results of the
previous experiments, the coin is suddenly approved as an acceptable
solution in the last experiment, which suggested a danger of partiality
(i.e., a risk for violation of distributional fairness) on the part of
the decision maker. Thus people may think it is not fair to
use a coin in situations where proper arguments for either
option can be advanced; but it is fair in a situation where it
is important to shield the decision from being influenced by
improper arguments. In other words, the randomizer is not seen
as an instrument promoting justice, but preventing injustice to
prevail.

The last issue explored in our experiments was whether one
randomizer is as good (or as bad) as any other. From a formal point of
view, the answer to this question must, by definition, be yes, as long
as the outcomes are truly independent and unbiased. However, as
mentioned in the introduction, the criteria for randomness may be hard
to specify and to test (Bar-Hillel & Wagenaar, 1993). In practice,
people might have preferences for procedures where the random element
is disguised (as in the penalty kick example), but when directly
confronted with the question (in Experiment 9) they preferred the coin
toss to the other suggested procedures, in respect to both randomness
and fairness. Even more telling are perhaps the results of Experiment
8, showing that participants are actually prepared to embrace random
procedures as long as they are abstractly described. Thus they seem to
approve the principle, but hate the practice. In this respect they are
a little like those of us who love humanity but detest people.

The present studies have demonstrated a robust and apparently deeply
ingrained reluctance against a chance device like the coin for making
an important decision. Yet, people seem to appreciate the usefulness
of a random procedure, on an abstract level, to solve a problem of
indeterminacy, but experience problems with applying a concrete
instantiation of this principle, which seems only tolerable to protect
the decision against unwanted partiality. Such ambivalence, in turn,
leads to conditions of what Beattie et al. (1994) termed “decision
aversion”. They report an experiment in which participants had to
imagine serving as a trustee for the estate of Mary who had two
daughters. Mary’s money and possessions were divided equally between
the two daughters except for a priceless antique grand piano. Being in
the role of the trustee, participants were asked which of three
conditions they would have preferred to be in: (A) Someone you know
would flip the coin to determine who will get the piano. (B) You
decide which daughter gets the piano. (C) It does not matter. (A) and
(B) are equally preferable, but were chosen only by a minority. The
results showed that 63% of the participants opted for (A) and only
29% for (B), which the authors interpreted as an indication of
decision aversion.

While being a viable interpretation, it is not in contradiction with
the pattern of results presented here and is compatible with our
explanations. There are several fundamental differences between the
experiment of Beattie et al. and ours. First, the outcome (who will
get the piano) is of intermediate importance and in this respect
resembles more the first author scenario employed in Experiment
4. But, most important, the coin flip in Beattie et al.’s experiment
is to be carried out by someone else. This implies that the decision
maker transfers the responsibility not only to the coin but, at the
same time, to another person who flips the coin. In contrast, in both
the accident and the kidney scenarios, one is confronted with the
option of flipping the coin which implies on one hand surrendering
control and responsibility and yet, after the outcome is known, one
may still feel responsible (and regret) for flipping the coin that led
to a particular outcome (and, legally be accountable for the
outcome).5

The judgment-decision discrepancy observed in the present studies
highlights the fact that judgments and choice decisions carry different
implications and may not be based on exactly the same considerations.
Judgments can be viewed as a predominantly cognitive process, whereas
choices and decisions are actions. As such, they can have more serious
consequences and are often (like in the present case) irreversible.
They are also associated with a higher degree of commitment,
responsibility, and occasional regret (Einhorn & Hogarth, 1981).
Because of their behavioral consequences, decisions are more likely
than judgments to be censured and sanctioned. For these reasons, it can
be expected that people are more careful and strict in their choices
than in their judgments (Ganzach, 1995).

To bridge the gap between judgments and decisions, people often rely
on guidelines that can be described as explicit judgment-decision
links. For instance, in criminal cases the rule is that the defendant
should only be convicted if he is judged to be guilty “beyond
reasonable doubt” (admittedly, as noted by Saunders and Genser
[1999], this is an ambiguous criterion). Action rules typically advise
people not to take chances, but to strive for some degree of
conviction or certainty before executing their favored plans. Less
often, explicit guidelines are offered for what action to take in case
of judgments of indeterminacy. As we already proposed, using a
randomizer is not incompatible with economic rational choice theory,
but it is not explicitly prescribed, as people are assumed to always
have preferences, however tiny ones. In contrast, game theory
explicitly recommends coin flip in games with more than one
equilibrium point (e.g., Rasmusen 1989). In more informal contexts,
people find it more natural to respond to indeterminacy with inaction
and deferral of choice.

The scenarios explored in the present experiments, describing
emergency situations, did not allow for this option, which would have
been the natural way out under other, less critical
circumstances. They are accordingly faced with a choice between two
unattractive strategies: Transferring the choice to a random device,
or forcing themselves to form a preference for one of two equally
justifiable options. The last strategy has the advantage of being
rational in the sense of being governed by a continued search for
reasons, the disadvantage being that this extended search will have to
give some reasons more than their proper weight. The first strategy is
more radical, by explicitly acknowledging the limits of reason-based
rationality, and by finding both sets of reasons equally valid and
equally strong cancelling them all. Decision by use of randomizer
might therefore look like a sacrifice of reason, control, and even
responsibility. To appear acceptable, higher principles must be
invoked, like non-partiality and offering everybody the same chance.

The use of a coin for solving a decision problem can be regarded as an
extreme example of assistance by a mechanical decision aid. It is well
known that such procedures are viewed with suspicion by decision makers
and their clients alike, even in areas where their superiority can be
documented (Sieck & Arkes, 2005). In the case of the coin, no such
superiority can be claimed. By definition, randomizers perform no
better than chance. They cannot even claim consistency, one coin toss
being uncorrelated with the next one. Added to this is the problem of
responsibility and accountability. If we grant that the decision maker
can be made morally responsible for an important choice (like which
patient should be given priority), he or she will also be responsible
for the decision to use a coin, which is an action that (as we have
seen) under some conditions can be justifiable. But who is responsible
for the outcome of the coin toss? Normally, one only thinks
of persons as responsible agents. Moreover, people are
traditionally only made accountable for consequences they could have
controlled and foreseen (Fischer & Ravizza, 1998). This makes
responsibility in the case of randomizers a very tricky issue and
should be the subject of further studies.

We mentioned already that a major cause for rejecting randomizers
is that from early childhood we are raised with the conviction that
everything must have an explanation, this is the reason-based approach
documented by Shafir et al. (1993). This belief is also represented in
the judicial system in the often cited aphorism of Lord Hewart from
Rex vs. Sussex: “It is not merely of some
importance, but is of fundamental importance, that justice should not
only be done, but should manifestly and undoubtedly be seen to be
done.”6 Thus, while a coin, or any other randomizer, provides
indisputable distribution fairness, it does not offer fairness that
can be “manifestly seen”. Most probably, it is because of these
reasons that the coin is rejected on what we termed procedural
grounds. Both the judicial system and lay people are reluctant to
accept that under some circumstances no rational reasons can be
unequivocally advanced in one way or another. It is because of this
boundless belief that “God does not play dice” and
that, therefore, every decision can and should be backed by some
reason, that Elster (1989) concluded that “rather than accept the
limits of reason, we prefer the rituals of reason” (p. 37).

Some of the results reported here, specifically the strong and deep
rooted repulsion to use of randomizers as decision sida, may seem to
some readers as not very surprising.7 Yet,
they have important theoretical and practical implications. One
concerns a limitation of choice theory, normative or descriptive, in
dealing with situations of indifference and indeterminacy. Despite the
ever increasing literature on behavioral choice theory, there are
hardly any studies that directly investigate authentic situations of
indeterminacy, in particular when the major relevant dimensions of the
choice set are non-compensatory. The present paper may offer a
starting point for a more rigorous examination of situations of
indeterminacy.

Second, the present paper is closely linked to Bandura’s (1982)
assertion regarding the psychology of chance encounters and life
paths. Bandura’s pointed out that the more important and meaningful
events in our life (e.g., choosing a partner, developing a career) are
at the end of the analysis a chance event even though we do not
perceive them as such. As he noted, separate chains of events in a
chance encounter may have their own causal determinants yet their
interaction which lead to the final outcome are determined by a random
rather than a pre-designed process. In line with people’s denial
concerning the weight of the random component in determining life
paths, supposedly because they are unaware of hidden random processes,
the present experiments demonstrate an active and deliberate (i.e.,
conscious) attempt to resist the entry of such chance events into
important life events.

Finally, our experiments may also carry some practical
implications. We believe that in the situations we posed to our
participants, specifically the two major scenarios employed in our
experiments, the use of a randomizer is the most sensible action to
use. In particular, a coin is a fast and efficient decision device,
certainly in the particular scenarios we employed in which
procrastinations may result in the worst outcome (i.e., both victims
or both patients will die). Unlike human decision makers, appropriate
random procedures (like a fair coin) are not contaminated (Wilson &
Brekke, 1994) by unwarranted biases that may interfere in the decision
process in an undesired manner. The coin is not only fair (in terms of
distributional fairness) but, not less important, is perceived as
such. Finally, a coin (or any other randomizer) may be the most sound
choice procedure, in cases where the different dimensions are
non-compensatory (e.g., Luce et al., 1999), there are no decisive
clear considerations of how the different dimensions should be
weighed, and most important, the outcome is indivisible. Unless one
adopts Solomon’s judgment, the decision is a binary one with no
possibilities in between. Put in other words, perhaps we should
realize that, under some conditions, we should accept the limits of
rational choice theory, and be open for a procedure that is efficient,
fair, and defendable if we use a broad definition of what is meant by
rationality.

References

Agresti, A. (1996). An introduction to categorical data
analysis. New York: Wiley.

Ashenfelter, D. (2003, June 21). Judge disciplined for coin flip.
Detroit Free Press.

Bandura, A. (1982). The psychology of chance encounters and life
paths. American Psychologist, 37, 747–755.

Bandura, A. (1998). Explorations of fortuitous determinants of life
paths. Psychological Inquiry, 9, 95–99.

Bar-Hillel, M. & Wagenaar, W. A. (1993). The perception of randomness.
In G. Keren & C. Lewis (Eds.), A handbook for data
analysis in the behavioral sciences: Methodological issues (pp.
369–394). Hillsdale, NJ: Lawrence Erlbaum.

Baron, J. & Spranca, M. (1987). Protected values.
Organizational Behavior and Human Decision Processes, 70,
1–16.

Beattie, J., Baron, J., Hershey, J. C. & Spranca, M. D. (1994).
Psychological determinants of decision attitude. Journal of
Behavioral Decision Making, 7, 129–144.

Broome, J. R. (1984). Selecting people randomly. Ethics, 95,
38–55.

Einhorn, H. J. & Hogarth, R. M. (1981). Behavioral decision theory:
Processes of judgment and choice. Annual Review of
Psychology, 32, 53–88

Ekeland, I. (1991). The broken dice. Chicago: The University of
Chicago Press.

Elster, J. (1989). Solomonic judgments: Studies in the
limitations of rationality. Cambridge: Cambridge University Press.

Falk, R. (1991). Randomness — an ill-defined, but much needed concept.
Journal of Behavioral Decision Making, 4, 215–218.

Falk, R. & Konold, C. (1997). Making sense of randomness: Implicit
encoding as a basis for judgment. Psychological Review,
104, 301–318.

Fischer, J. M. & Ravizza, M. (1998). Responsibility and
control: A theory of moral responsibility. Cambridge: Cambridge
University Press.

Ganzach, Y. (1995). Attribute scatter and decision outcome: Judgment
versus choice. Organizational Behavior and Human Decision
Processes, 62, 113–122.

Hsee, C. K. (1996). The evaluability hypothesis: an explanation for
preference reversals between joint and separate evaluations of
alternatives. Organizational Behavior and Human Decision
Processes, 67, 247–257.

Hsee, C. K., Loewenstein, G. F., Blount, S., & Bazerman, M. H. (1999).
Preference reversals between joint and separate evaluations of
options: a review and theoretical analysis. Psychological
Bulletin, 125, 576–590.

Luce, M. F., Payne, J.W. & Bettman, J.R. (1999). Emotional tradeoff
difficulty and choice. Journal of Marketing Research, 36,
43–159.

Neuringer, A. (1986). Can people behave “randomly”? The role of
feedback. Journal of Experimental Psychology: General, 115,
62–75.

Oberholzer-Gee, F., Bohnet, I. & Frey, B.S. (1997). Fairness and
competence in democratic decisions. Public Choice, 91,
89–105.

Pashley, P.J. (1993). On generating random sequences. In G. Keren & C.
Lewis (Eds.). A handbook for data analysis in the
behavioral sciences: Methodological issues. Hillsdale, NJ:
Lawrence Erlbaum.

Rasmusen, E. (1989) Games and Information: An Introduction to
Game Theory. Cambridge: Basil Blackwell.

Resnik, J. (1985). Precluding appeals. Cornell Law Review, 70,
1–16.

Saunders, H. D. and Genser, J. G. (1999) Trial and error. The
Sciences, September/October issue.

Shafir, E., Simonson, I. & Tversky, A. (1993). Reason-based choice.
Cognition, 49, 11–36.

Sieck, W. R. & Arkes, H. R. (2005). The recalcitrance of overconfidence
and its contribution to decision aid neglect. Journal of
Behavioral Decision Making, 18, 29–53.

Skinner, E. A. (1996). A guide to constructs of control. Journal
of Personality and Social Psychology, 71, 549–570.

Tetlock, P. E. (1992). The impact of accountability on judgment and
choice: Toward a social contingency model. In M.P. Zanna (Ed.),
Advances in Experimental Social Psychology, 24 (pp. 331–376).
New York: Academic Press.

Trope, Y. & Liberman, N. (2003). Temporal construal.
Psychological Review, 110, 403–421.

Vallacher, R. R. & Wegner, D. M. (1987). What do people think they are
doing? Action identification and human behavior.
Psychological Review, 94, 3–15.

Wilson, T. D., & Brekke, N. (1994) Mental contamination and mental
correction: Unwanted influences on judgments and evaluations. Psychological
Bulletin, 116, 117–142.

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